On the implementation of flux limiters in algebraic frameworks

The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are paramount importance for temporal integration high-speed aerodynamics, multiphase flows hyperbolic equations in general. Meanwhile, breakthrough new architectures hybridization supercomputer systems pose a huge portability challenge, particularly legacy codes, since subroutines that form algorithms, so-called kernels, must be adapted various complex parallel programming paradigms. From this perspective, development innovative implementations relying on minimalist set kernels simplifies deployment software state-of-the-art supercomputers, while it requires reformulation such as aforementioned limiters. Equipped with basic algebraic topology graph theory underlying classical mesh concept, limiter formulation presented based adoption data structures kernels. As result, traditional cast into stream only two types kernels: sparse matrix-vector multiplication generalized pointwise binary operators. newly proposed eases numerical technique massively parallel, potentially hybrid, demonstrated canonical advection problem.